Suppose you wanted to "pull an Einstein," and create a static universe  in which the gravitational attraction of matter is exactly balanced by the gravitational repulsion of dark energy with equation-of-state parameter − 1/ 3 < wq < − 1 and energy density εq.

What is the necessary matter density (εm) required to produce a static universe, expressed in terms of εq and wq?

Will the curvature of this static universe be negative or positive?

What will be its radius of curvature, expressed in terms of εq and wq?

An airplane flying parallel to the ground undergoes two consecutive displacements. the first is 76 km at 39.8◦ west of north, and the second is 156 km at 59.9◦ east of north. what is the magnitude of the plane’s total displacement? answer in units of km. 020 (part 2 of 2) 10.0

Calculate the ratio of h+ ions to oh– ions at a ph = 6. find the concentration of h+ ions to oh– ions listed in table b of your student guide. then divide the h+ concentration by the oh– concentration. record this calculated ratio in table a of your student guide. compare your approximated and calculated ratios of h+ ions to oh– ions at a ph = 6. are they the same? why or why not? record your explanation in table a. what is the concentration of h+ ions at a ph = 6? mol/l what is the concentration of oh– ions at a ph = 6? mol/l what is the ratio of h+ ions to oh– ions at a ph = 6? : 1

Adolphin emits ultrasound at 100khz and uses the timing of reflections to determine the position of objects in the water. part a what is the wavelength of this ultrasound? assume that temperature of water is 20 degrees c. answer in cm